tuple_tgammaTupleTgammaTupleTgammatuple_tgammatuple_tgamma🔗

Short description🔗

tuple_tgammaTupleTgammaTupleTgammatuple_tgammatuple_tgamma — Compute the gamma function of a tuple.

Signature🔗

tuple_tgamma( number T, out number Gamma )

HTuple HTuple::TupleTgamma( ) const

HTuple HTuple.TupleTgamma( )

Description🔗

tuple_tgammaTupleTgamma computes the gamma function of the input tuple Ttt. The gamma function is defined as:

\[\begin{eqnarray*} \Gamma(x) = \int_{0}^{\infty} t^{x-1} e^{-t} dt . \end{eqnarray*}\]

It is defined for every real number except for nonpositive integers. For nonnegative integer \(m\), it holds that

\[\begin{eqnarray*} \Gamma(m+1) = m! \end{eqnarray*}\]

and, more generally, for all \(x\):

\[\begin{eqnarray*} \Gamma(x+1) = x \Gamma(x) . \end{eqnarray*}\]

The value of the gamma function is always returned as a floating point number in Gammagammagamma. The gamma function of a string is not allowed.

Exception: Empty input tuple🔗

If the input tuple is empty, the operator returns an empty tuple.

HDevelop In-line Operation🔗

HDevelop provides an in-line operation for tuple_tgammaTupleTgamma, which can be used in an expression in the following syntax:

Gamma := tgamma(T)

Execution information🔗

Execution information

Multithreading type: reentrant (runs in parallel with non-exclusive operators).
Multithreading scope: global (may be called from any thread).
Processed without parallelization.

Parameters🔗

Ttt (input_control) number(-array) → (real / integer)HTuple (double / Hlong)HTuple (double / int / long)MaybeSequence[Union[float, int]]Htuple (double / Hlong)

Input tuple.

Gammagammagamma (output_control) number(-array) → (real)HTuple (double)HTuple (double)Sequence[float]Htuple (double)

Value of the gamma function of the input tuple.

Combinations with other operators🔗

Combinations

Alternatives

tuple_lgammaTupleLgamma

Module🔗

Foundation